Relatively speaking, at the local region of any open system, order is seemed to be realized but there is always some amount of energy loss in the form of heat to the environment.

If we shuffle a brand new ordered deck of cards, we need to spend energy. The more we shuffle the more random is the deck of cards but the more energy is spended. The increase in randomness of the deck of cards is entropy. How much we have to shuffle to regain the original order of the deck of cards?

Energy flows from hot to cold.This is a net flow that has one space direction
and one time direction.CP and T are violated so CPT symmetry is restored.
The fact that no process has been found which breals CPT symmetry might just be because no process can break the second law of thermodynamics.

Space might be expanding i.e dark energy increasing, because
dark energy has entropy that increases with time - that is to say:
dark energy has energy microstates.If it does have microstates then it
could absorb energy from other particles in the universe e.g microwave background photons.

I'm just suggesting that dark energy if it has microstates could be absorbing nergy from photons and other particles in the universe.It is my belief that dark energy + vacuum particle energy + energy of antimatter = constant if dark energy is made from vacuum energy and/or antimatter enrgy.

Is microstate the same as a wave function, [itex] \psi [/itex]? If it is, this implies that dark energy can be derived from Dirac's relativistic equation as the negative square root of [itex] E^2 = c^2 \vec{p}^2 + m^2 c^4[/itex].

What information does this complex conjugate of the energy operator carry in relativistic quantum mechanics - any information about dark energy is useful information to me.I expect dark energy to be non-uniform because if it can come from other energy sources in the universe, then since no other enrgy source in the universe can be uniformly distributed throughout it,dark energy shouldn't be either.

What information does this complex conjugate of the energy operator carry in relativistic quantum mechanics - any information about dark energy is useful information to me.I expect dark energy to be non-uniform because if it can come from other energy sources in the universe, then since no other enrgy source in the universe can be uniformly distributed throughout it,dark energy shouldn't be either.

This was already used by Dirac to explain the existence of antimatter.

If you limit yourself to SR approaches, you limit yourself to further explanations on the nature of the geometries. If you join electromagnetism and Gravity, there is a result theoretically, and a geometry, that helps you move forward.

Dirac could not give any geometric interpretation. The best he did was the sea of negative energy.

My interpretation for [itex]E^2[/itex] is the existence of two distinct topologies of fully twisted Moebius strip. And with your suggestion, and I already mentioned in other posts, the spin is related to the genus of the topologies.

I think, at first many physicists, no doubt, thought that dark energy should come from antimatter. But the problem is antimatter cannot be found globally. Locally, it happens at quantum fluctuations of the vacuum and high energy domains in particle accelerators. But the vacuum is highly uniform because of the isotropy and homogeneity of the cosmos regardless of the existence of stars and galaxies and other interstellar or intergalactic gases and nebulae.

Antimatter cannot be found globally if nearly all of it has already become dark energy.
This suggests the universe will stop accelerating soon and the dark energy density
will decrease as antimatter reforms from dark energy.